TheGI1: Grundlagen und Algebraische Strukturen Schriftliche ...

8/10
ΣCont Set String
data Setdata � [0, 9] String data � [0, 9]
cont Setcont � P ([0, 9]) String cont � [0, 9] ∗
z : ( data ) zSet : Setdata zString : String data
zSet � 0 zString � 0
empty : ( cont ) empty Set : Setcont empty String : String cont
empty Set � ∅ empty String � λ
s : ( data, data ) sSet : Setdata → Setdata sString : String data → String data
x ↦→ (x + 1) mod 10 x ↦→ (x + 1) mod 10
insert : ( data, cont, cont ) insertSet : Setdata × Setcont → Setcont insertString : String data × String cont → String cont
( x, s ) ↦→ { x } ∪ s ( x, v ) ↦→ v · x
union : ( cont, cont, cont ) unionSet : Setcont × Setcont → Setcont unionString : String cont × String cont → String cont
( s, t ) ↦→ s ∪ t ( v, w ) ↦→ v · w
X � (Xs) s∈{ data, cont }
Xdata � { d1, d2, d3 }
Xcont � { c1, c2 }
α : X → String
α � (αs : Xs → String s ) s∈{ data, cont }
αdata � { ( d1, 6 ), ( d2, 4 ), ( d3, 1 ) }
αcont � { ( c1, 7658 ), ( c2, 12 ) }
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